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Prove that the row vectors of an nxn invertible matrix A form a basis for R".

Prove that the row vectors of an nxn invertible matrix A form a basis for R".

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. Prove that the row vectors of an nx n invertible matrix A form a basis for R". Hin: Again, there are several ways to do this. One way is to observe that if A is invertible, then the reduced row echelon form of A is . Hence RS(A) = RS(I,) = R". Hence the row vectors of A span R". It follows that the row vectors of A form a basis for R". Justify this argument by citing the appropriate theorems in the textbook for the course or devise an argument of your own.
Transcribed Image Text:2. Prove that the row vectors of an nx n invertible matrix A form a basis for R". Hin: Again, there are several ways to do this. One way is to observe that if A is invertible, then the reduced row echelon form of A is . Hence RS(A) = RS(I,) = R". Hence the row vectors of A span R". It follows that the row vectors of A form a basis for R". Justify this argument by citing the appropriate theorems in the textbook for the course or devise an argument of your own.
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